Chapter A.2, Problem 24E

Solution

To expand the product ${\left(3-5x\right)}^2$ .

  $25x^2-30x+9$

Given:

The expression, ${\left(3-5x\right)}^2$

Concept Used:

• Like terms are the terms that contain the same variable with similar exponents on it. Constants are like terms as well.
• In any expression, terms are separated by plus or minus signs.
• Coefficients are the constants in front of the variable terms.
• ${\left(a-b\right)}^2=a^2+b^2-2ab$

Calculation:

In order to expand the product first expand expand the brackets by using the formula ${\left(a-b\right)}^2=a^2+b^2-2ab$ and simplify by collecting like terms as shown below:

  $\begin{array}{c}{\left(3-5x\right)}^2={\left(3\right)}^2+{\left(5x\right)}^2-2\cdot 3\cdot 5x\\ =9+25x^2-30x\\ =25x^2-30x+9\end{array}$

So, the expression is $25x^2-30x+9$ .